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Reduced Temperature using Peng Robinson Equation given Reduced and Critical Parameters Calculator

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✖Reduced Pressure is the ratio of the actual pressure of the fluid to its critical pressure. It is dimensionless.ⓘ Reduced Pressure [Pr]
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✖Critical Pressure is the minimum pressure required to liquify a substance at the critical temperature.ⓘ Critical Pressure [Pc]
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✖Peng–Robinson parameter a is an empirical parameter characteristic to equation obtained from Peng–Robinson model of real gas.ⓘ Peng–Robinson Parameter a [aPR]
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✖α-function is a function of temperature and the acentric factor.ⓘ α-function [α]
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✖Reduced Molar Volume of a fluid is computed from the ideal gas law at the substance's critical pressure and temperature per mole.ⓘ Reduced Molar Volume [Vm,r]
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✖Critical Molar Volume is the volume occupied by gas at critical temperature and pressure per mole.ⓘ Critical Molar Volume [Vm,c]
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✖Peng–Robinson parameter b is an empirical parameter characteristic to equation obtained from Peng–Robinson model of real gas.ⓘ Peng–Robinson Parameter b [bPR]
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✖Critical Temperature is the highest temperature at which the substance can exist as a liquid. At this phase boundaries vanish, and the substance can exist both as a liquid and vapor.ⓘ Critical Temperature [Tc]
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✖Reduced Temperature is the ratio of the actual temperature of the fluid to its critical temperature. It is dimensionless.ⓘ Reduced Temperature using Peng Robinson Equation given Reduced and Critical Parameters [Tr]
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Reduced Temperature using Peng Robinson Equation given Reduced and Critical Parameters

Formula
`"T"_{"r"} = ((("P"_{"r"}*"P"_{"c"})+((("a"_{"PR"}*"α")/((("V"_{"m,r"}*"V"_{"m,c"})^2)+(2*"b"_{"PR"}*("V"_{"m,r"}*"V"_{"m,c"}))-("b"_{"PR"}^2)))))*((("V"_{"m,r"}*"V"_{"m,c"})-"b"_{"PR"})/"[R]"))/"T"_{"c"}`

Example
`"0.000192"=((("3.675E^-5"*"218Pa")+((("0.1"*"2")/((("11.2"*"11.5m³/mol")^2)+(2*"0.12"*("11.2"*"11.5m³/mol"))-(("0.12")^2)))))*((("11.2"*"11.5m³/mol")-"0.12")/"[R]"))/"647K"`

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Reduced Temperature using Peng Robinson Equation given Reduced and Critical Parameters Solution

STEP 0: Pre-Calculation Summary
Formula Used
Reduced Temperature = (((Reduced Pressure*Critical Pressure)+(((Peng–Robinson Parameter a*α-function)/(((Reduced Molar Volume*Critical Molar Volume)^2)+(2*Peng–Robinson Parameter b*(Reduced Molar Volume*Critical Molar Volume))-(Peng–Robinson Parameter b^2)))))*(((Reduced Molar Volume*Critical Molar Volume)-Peng–Robinson Parameter b)/[R]))/Critical Temperature
Tr = (((Pr*Pc)+(((aPR*α)/(((Vm,r*Vm,c)^2)+(2*bPR*(Vm,r*Vm,c))-(bPR^2)))))*(((Vm,r*Vm,c)-bPR)/[R]))/Tc
This formula uses 1 Constants, 9 Variables
Constants Used
[R] - Universal gas constant Value Taken As 8.31446261815324
Variables Used
Reduced Temperature - Reduced Temperature is the ratio of the actual temperature of the fluid to its critical temperature. It is dimensionless.
Reduced Pressure - Reduced Pressure is the ratio of the actual pressure of the fluid to its critical pressure. It is dimensionless.
Critical Pressure - (Measured in Pascal) - Critical Pressure is the minimum pressure required to liquify a substance at the critical temperature.
Peng–Robinson Parameter a - Peng–Robinson parameter a is an empirical parameter characteristic to equation obtained from Peng–Robinson model of real gas.
α-function - α-function is a function of temperature and the acentric factor.
Reduced Molar Volume - Reduced Molar Volume of a fluid is computed from the ideal gas law at the substance's critical pressure and temperature per mole.
Critical Molar Volume - (Measured in Cubic Meter per Mole) - Critical Molar Volume is the volume occupied by gas at critical temperature and pressure per mole.
Peng–Robinson Parameter b - Peng–Robinson parameter b is an empirical parameter characteristic to equation obtained from Peng–Robinson model of real gas.
Critical Temperature - (Measured in Kelvin) - Critical Temperature is the highest temperature at which the substance can exist as a liquid. At this phase boundaries vanish, and the substance can exist both as a liquid and vapor.
STEP 1: Convert Input(s) to Base Unit
Reduced Pressure: 3.675E-05 --> No Conversion Required
Critical Pressure: 218 Pascal --> 218 Pascal No Conversion Required
Peng–Robinson Parameter a: 0.1 --> No Conversion Required
α-function: 2 --> No Conversion Required
Reduced Molar Volume: 11.2 --> No Conversion Required
Critical Molar Volume: 11.5 Cubic Meter per Mole --> 11.5 Cubic Meter per Mole No Conversion Required
Peng–Robinson Parameter b: 0.12 --> No Conversion Required
Critical Temperature: 647 Kelvin --> 647 Kelvin No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Tr = (((Pr*Pc)+(((aPR*α)/(((Vm,r*Vm,c)^2)+(2*bPR*(Vm,r*Vm,c))-(bPR^2)))))*(((Vm,r*Vm,c)-bPR)/[R]))/Tc --> (((3.675E-05*218)+(((0.1*2)/(((11.2*11.5)^2)+(2*0.12*(11.2*11.5))-(0.12^2)))))*(((11.2*11.5)-0.12)/[R]))/647
Evaluating ... ...
Tr = 0.000191927963004368
STEP 3: Convert Result to Output's Unit
0.000191927963004368 --> No Conversion Required
FINAL ANSWER
0.000191927963004368 ≈ 0.000192 <-- Reduced Temperature
(Calculation completed in 00.004 seconds)
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Home » Chemistry » Kinetic Theory of Gases » Real Gas » Peng Robinson Model of Real Gas » Reduced Temperature » Reduced Temperature using Peng Robinson Equation given Reduced and Critical Parameters

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7 Reduced Temperature Calculators

Reduced Temperature using Peng Robinson Equation given Reduced and Critical Parameters
Go Reduced Temperature = (((Reduced Pressure*Critical Pressure)+(((Peng–Robinson Parameter a*α-function)/(((Reduced Molar Volume*Critical Molar Volume)^2)+(2*Peng–Robinson Parameter b*(Reduced Molar Volume*Critical Molar Volume))-(Peng–Robinson Parameter b^2)))))*(((Reduced Molar Volume*Critical Molar Volume)-Peng–Robinson Parameter b)/[R]))/Critical Temperature
Reduced Temperature using Peng Robinson Equation given Critical and Actual Parameters
Go Reduced Temperature = ((Pressure+(((Peng–Robinson Parameter a*α-function)/((Molar Volume^2)+(2*Peng–Robinson Parameter b*Molar Volume)-(Peng–Robinson Parameter b^2)))))*((Molar Volume-Peng–Robinson Parameter b)/[R]))/Critical Temperature
Reduced Temperature given Peng Robinson Parameter a, and other Actual and Reduced Parameters
Go Reduced Temperature = Temperature/(sqrt((Peng–Robinson Parameter a*(Pressure/Reduced Pressure))/(0.45724*([R]^2))))
Reduced Temperature given Peng Robinson Parameter b, other Actual and Reduced Parameters
Go Reduced Temperature = Temperature/((Peng–Robinson Parameter b*(Pressure/Reduced Pressure))/(0.07780*[R]))
Reduced Temperature given Peng Robinson Parameter a, and other Actual and Critical Parameters
Go Temperature of Gas = Temperature/(sqrt((Peng–Robinson Parameter a*Critical Pressure)/(0.45724*([R]^2))))
Reduced Temperature given Peng Robinson Parameter b, other Actual and Critical Parameters
Go Reduced Temperature = Temperature/((Peng–Robinson Parameter b*Critical Pressure)/(0.07780*[R]))
Reduced Temperature for Peng Robinson Equation using Alpha-function and Pure Component Parameter
Go Reduced Temperature = (1-((sqrt(α-function)-1)/Pure Component Parameter))^2

Reduced Temperature using Peng Robinson Equation given Reduced and Critical Parameters Formula

Reduced Temperature = (((Reduced Pressure*Critical Pressure)+(((Peng–Robinson Parameter a*α-function)/(((Reduced Molar Volume*Critical Molar Volume)^2)+(2*Peng–Robinson Parameter b*(Reduced Molar Volume*Critical Molar Volume))-(Peng–Robinson Parameter b^2)))))*(((Reduced Molar Volume*Critical Molar Volume)-Peng–Robinson Parameter b)/[R]))/Critical Temperature
Tr = (((Pr*Pc)+(((aPR*α)/(((Vm,r*Vm,c)^2)+(2*bPR*(Vm,r*Vm,c))-(bPR^2)))))*(((Vm,r*Vm,c)-bPR)/[R]))/Tc

What are Real Gases?

Real gases are non ideal gases whose molecules occupy space and have interactions; consequently, they do not adhere to the ideal gas law. To understand the behavior of real gases, the following must be taken into account:
- compressibility effects;
- variable specific heat capacity;
- van der Waals forces;
- non-equilibrium thermodynamic effects;
- issues with molecular dissociation and elementary reactions with variable composition.

How to Calculate Reduced Temperature using Peng Robinson Equation given Reduced and Critical Parameters?

Reduced Temperature using Peng Robinson Equation given Reduced and Critical Parameters calculator uses Reduced Temperature = (((Reduced Pressure*Critical Pressure)+(((Peng–Robinson Parameter a*α-function)/(((Reduced Molar Volume*Critical Molar Volume)^2)+(2*Peng–Robinson Parameter b*(Reduced Molar Volume*Critical Molar Volume))-(Peng–Robinson Parameter b^2)))))*(((Reduced Molar Volume*Critical Molar Volume)-Peng–Robinson Parameter b)/[R]))/Critical Temperature to calculate the Reduced Temperature, The Reduced Temperature using Peng Robinson Equation given Reduced and Critical Parameters formula is defined as the actual temperature of the fluid to its critical temperature. It is dimensionless. Reduced Temperature is denoted by Tr symbol.

How to calculate Reduced Temperature using Peng Robinson Equation given Reduced and Critical Parameters using this online calculator? To use this online calculator for Reduced Temperature using Peng Robinson Equation given Reduced and Critical Parameters, enter Reduced Pressure (Pr), Critical Pressure (Pc), Peng–Robinson Parameter a (aPR), α-function (α), Reduced Molar Volume (Vm,r), Critical Molar Volume (Vm,c), Peng–Robinson Parameter b (bPR) & Critical Temperature (Tc) and hit the calculate button. Here is how the Reduced Temperature using Peng Robinson Equation given Reduced and Critical Parameters calculation can be explained with given input values -> 0.000192 = (((3.675E-05*218)+(((0.1*2)/(((11.2*11.5)^2)+(2*0.12*(11.2*11.5))-(0.12^2)))))*(((11.2*11.5)-0.12)/[R]))/647.

FAQ

What is Reduced Temperature using Peng Robinson Equation given Reduced and Critical Parameters?
The Reduced Temperature using Peng Robinson Equation given Reduced and Critical Parameters formula is defined as the actual temperature of the fluid to its critical temperature. It is dimensionless and is represented as Tr = (((Pr*Pc)+(((aPR*α)/(((Vm,r*Vm,c)^2)+(2*bPR*(Vm,r*Vm,c))-(bPR^2)))))*(((Vm,r*Vm,c)-bPR)/[R]))/Tc or Reduced Temperature = (((Reduced Pressure*Critical Pressure)+(((Peng–Robinson Parameter a*α-function)/(((Reduced Molar Volume*Critical Molar Volume)^2)+(2*Peng–Robinson Parameter b*(Reduced Molar Volume*Critical Molar Volume))-(Peng–Robinson Parameter b^2)))))*(((Reduced Molar Volume*Critical Molar Volume)-Peng–Robinson Parameter b)/[R]))/Critical Temperature. Reduced Pressure is the ratio of the actual pressure of the fluid to its critical pressure. It is dimensionless, Critical Pressure is the minimum pressure required to liquify a substance at the critical temperature, Peng–Robinson parameter a is an empirical parameter characteristic to equation obtained from Peng–Robinson model of real gas, α-function is a function of temperature and the acentric factor, Reduced Molar Volume of a fluid is computed from the ideal gas law at the substance's critical pressure and temperature per mole, Critical Molar Volume is the volume occupied by gas at critical temperature and pressure per mole, Peng–Robinson parameter b is an empirical parameter characteristic to equation obtained from Peng–Robinson model of real gas & Critical Temperature is the highest temperature at which the substance can exist as a liquid. At this phase boundaries vanish, and the substance can exist both as a liquid and vapor.
How to calculate Reduced Temperature using Peng Robinson Equation given Reduced and Critical Parameters?
The Reduced Temperature using Peng Robinson Equation given Reduced and Critical Parameters formula is defined as the actual temperature of the fluid to its critical temperature. It is dimensionless is calculated using Reduced Temperature = (((Reduced Pressure*Critical Pressure)+(((Peng–Robinson Parameter a*α-function)/(((Reduced Molar Volume*Critical Molar Volume)^2)+(2*Peng–Robinson Parameter b*(Reduced Molar Volume*Critical Molar Volume))-(Peng–Robinson Parameter b^2)))))*(((Reduced Molar Volume*Critical Molar Volume)-Peng–Robinson Parameter b)/[R]))/Critical Temperature. To calculate Reduced Temperature using Peng Robinson Equation given Reduced and Critical Parameters, you need Reduced Pressure (Pr), Critical Pressure (Pc), Peng–Robinson Parameter a (aPR), α-function (α), Reduced Molar Volume (Vm,r), Critical Molar Volume (Vm,c), Peng–Robinson Parameter b (bPR) & Critical Temperature (Tc). With our tool, you need to enter the respective value for Reduced Pressure, Critical Pressure, Peng–Robinson Parameter a, α-function, Reduced Molar Volume, Critical Molar Volume, Peng–Robinson Parameter b & Critical Temperature and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
How many ways are there to calculate Reduced Temperature?
In this formula, Reduced Temperature uses Reduced Pressure, Critical Pressure, Peng–Robinson Parameter a, α-function, Reduced Molar Volume, Critical Molar Volume, Peng–Robinson Parameter b & Critical Temperature. We can use 5 other way(s) to calculate the same, which is/are as follows -
  • Reduced Temperature = (1-((sqrt(α-function)-1)/Pure Component Parameter))^2
  • Reduced Temperature = Temperature/(sqrt((Peng–Robinson Parameter a*(Pressure/Reduced Pressure))/(0.45724*([R]^2))))
  • Reduced Temperature = Temperature/((Peng–Robinson Parameter b*Critical Pressure)/(0.07780*[R]))
  • Reduced Temperature = Temperature/((Peng–Robinson Parameter b*(Pressure/Reduced Pressure))/(0.07780*[R]))
  • Reduced Temperature = ((Pressure+(((Peng–Robinson Parameter a*α-function)/((Molar Volume^2)+(2*Peng–Robinson Parameter b*Molar Volume)-(Peng–Robinson Parameter b^2)))))*((Molar Volume-Peng–Robinson Parameter b)/[R]))/Critical Temperature
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